(1) 对称轴过点(1,0),方程为x = 1= -(-2)/(2a) = 1/a,a = 1
y = x^2 -2x +c = (x-1)^2 + c-1
图象向右平移一个单位后,二次函数方程为y = (x-1 -1)^2 + c -1 = (x-2)^2 + c - 1
经过坐标原点O:0 = (0-2)^2 + c -1,c = -3
二次函数为y = x^2 -2x -3
(2)D(0,1),B(3,0),DB斜率:-1/3
C(0,-3),BC斜率:1
E(1,-4),BE斜率:2
tgA = |[(-1/3 -1)/[1+(-1/3)*1]| = 2
tgB = |(2 -1)/(1+2*1)| = 1/3
tg(A - B) = (tgA - tgB)/(1 + tgAtgB) = (2 - 1/3)/(1 + 2*1/3) = 1
A - B = 45度
(3) P(1,a)
PA^2 = PC^2
(1+1)^2 + (a-0)^2 = (1-0)^2 + (a +3)^2
a = -1
P(1,-1)
PA^2 = 4+1 = 5
DB = √[(3-0)^2 + (0 -1)^2] = √10
三角形BDM的面积的值等于PA平方:
5 = (1/2)*DB*DB上的高
= DB上的高 * √10/2
DB上的高(M与BD的距离) = 10/√10 = √10
设M的坐标为(m,m^2 -2m -3),m>0
DB的方程为：y=-1/3x+1,改写为 x + 3y -3 =0
M与BD的距离:|m +3(m^2 -2m -3)|/√(1+3^2) = √10
|3m^2 -5m -12| = 10
3m^2 -5m -12 >= 0时：3m^2 -5m -12 = 10
3m^2 -5m -22 = 0
m = -2 (= 0）
3m^2 -5m -12＜0时：3m^2 -5m -12 = -10
3m^2 -5m -2 = 0
m = -1/3 (